论文标题
评估依赖性不确定性的非负多元风险的联合风险
On evaluation of joint risk for non-negative multivariate risks under dependence uncertainty
论文作者
论文摘要
在本文中，我们提出了一种新型的公理方法，以评估依赖性不确定性的多种保险风险的联合风险。由预期公用事业理论和Cobb-Dauglas实用程序函数的动机，我们为非负多元风险建立了联合风险措施，我们将其称为标量扭曲关节风险措施。研究了其基本属性后，我们通过提出一组新的公理来提供公理表征。最新的公理是组成部分的正同质性。然后，基于最终的失真关节风险度量，我们还提出了一类新的非负多元风险矢量值扭曲关节风险度量。最后，我们与文献中已知的一些矢量价值多元风险度量进行比较，例如在风险，多元可靠性的有条件尾部期望，多元尾巴有条件期望和多元变量造成扭曲风险措施的风险，多元可靠性的较低价值。事实证明，这些矢量值的多元风险度量分别具有矢量值扭曲关节风险措施的形式。本文主要给出一些关于依赖不确定性下关节风险的评估的理论结果，预计将有助于衡量关节风险。
In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish a joint risk measure for non-negative multivariate risks, which we refer to as a scalar distortion joint risk measure. After having studied its fundamental properties, we provide an axiomatic characterization of it by proposing a set of new axioms. The most novel axiom is the component-wise positive homogeneity. Then, based on the resulting distortion joint risk measures, we also propose a new class of vector-valued distortion joint risk measures for non-negative multivariate risks. Finally, we make comparisons with some vector-valued multivariate risk measures known in the literature, such as multivariate lower-orthant value at risk, multivariate upper-orthant conditional-tail-expectation, multivariate tail conditional expectation and multivariate tail distortion risk measures. It turns out that those vector-valued multivariate risk measures have forms of vector-valued distortion joint risk measures, respectively. This paper mainly gives some theoretical results about the evaluation of joint risk under dependence uncertainty, and it is expected to be helpful for measuring joint risk.
